Abstract: By Dubrovin--Zhang theory, there is a deep relation between dispersive deformations of the hierarchies of hydrodynamic type corresponding to Frobenius manifolds and the geometry of the moduli spaces of stable algebraic curves. I will talk about a generalization of some of the results of the Dubrovin--Zhang theory for flat F-manifolds, which we obtained in joint works with A. Arsie, P. Lorenzoni and P. Rossi.
